The optimal product mix and the total profit contribution A recommendation as to whether TJ, Inc., should purchase an additional 500 pounds of almonds for $500 from a supplier who overbought Recommendations on how profit contribution could be increased (if at all) if TJ, Inc., does not satisfy all existing orders
TJ, Inc., makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts.
In preparation for the fall season, TJ, Inc., purchased the following shipments of nuts:
|
Type of Nut |
Shipment Amount (pounds) |
|
Almond |
6000 |
|
Brazil |
7500 |
|
Filbert |
7500 |
|
Pecan |
6000 |
|
Walnut |
7500 |
The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25%filberts, 10% pecans, and 25% walnuts. The Deluxe Mix consists of 20% of each type of nut, and Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts.
An accountant at TJ, Inc., analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $1.85 for the Regular Mix, $2.10 for the Deluxe Mix, and $2.15 for the Holiday Mix. These figures do not include the cost of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets.
Customer orders already received are summarized here:
|
Type of Mix |
Orders (pounds) |
|
Regular |
10000 |
|
Deluxe |
3000 |
|
Holiday |
5000 |
Because demand is running high, TJ, Inc., expects to receive many more orders than can be satisfied.
TJ, Inc., is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to the Free Store. Even if it is not profitable to do so, the president of TJ, Inc., indicated that the orders already received must be satisfied.
Managerial Report
Perform an analysis of the TJ, Inc. product mix problem. Prepare a summary report of your findings for TJ, Inc.’s president. Be sure to include information and analysis on the following:
- The optimal product mix and the total profit contribution
- A recommendation as to whether TJ, Inc., should purchase an additional 500 pounds of almonds for $500 from a supplier who overbought
- Recommendations on how profit contribution could be increased (if at all) if TJ, Inc., does not satisfy all existing orders
You need to include linear programming model and sensitivity report into your managerial report.
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